Gather all ingredients. Preheat the oven to 400 degrees F (200 degrees C).

Press the pie crust into the bottom and up the sides of a 9-inch pie plate. Bake the pie shell for 3 to 5 minutes, just to firm it up, then remove from the oven, and set aside.

Place carrots in a saucepan with enough water to cover. Bring to a boil, and cook until tender, about 10 minutes.

Drain water, and mash carrots until smooth using a food processor, or potato ricer.

Combine carrot puree, sugar, and eggs together in a medium bowl; mix in cinnamon and vanilla. Gradually stir in the milk.

Pour mixture into the partially baked pie shell.

Bake for 10 minutes in the preheated oven, then reduce heat to 350 degrees F (175 degrees C). Continue to bake the pie until filling is firm, about 40 to 45 minutes. Cool completely before serving.